Question: $ \lim_{x\to 2}(x^3-5x^2+1)=$
Explanation: $x^3-5x^2+1$ defines a polynomial function. Polynomial functions are continuous across their entire domain, and their domain is all real numbers. In other words, for any polynomial $p$ and any possible input $c$, we know that this equality holds: $\lim_{x\to c}p(x)=p(c)$ Therefore, in order to find $ \lim_{x\to 2}(x^3-5x^2+1)$, we can simply evaluate $(x^3-5x^2+1)$ at $x=2$. $\begin{aligned} &\phantom{=}x^3-5x^2+1 \\\\ &=(2)^3-5(2)^2+1 \gray{\text{Substitute }x=2} \\\\ &=8-20+1 \\\\ &=-11 \end{aligned}$ In conclusion, $ \lim_{x\to 2}(x^3-5x^2+1)=-11$.